Abstract: With the rapid development of science and technology, in the twenty-first Century, many metals were used in the field of modern medicine, in which titanium and its alloys occupy half of the medical metal materials because of their advantages of high strength, low modulus of elasticity and good biocompatibility. Titanium dioxide（TiO₂） is the most widely used in vitro assisted treatment materials because of its excellent band structure, good chemical stability, high catalytic activity and low price. Based on the density functional theory, the first principle pseudopotential method is used to simulate the electrical parameters（forbidden band width, state density） and mechanical properties（elastic constants and elastic module） of different structures of TiO₂ and two element beta titanium alloy（Ti-Mo）. The results show that rutile TiO₂ is a direct semiconductor with a band gap of 2.03 eV, and anatase TiO₂ is an indirect semiconductor with a band gap of 2.15 eV. The calculation results of three Ti-Mo alloys of Ti15 Mo1, Ti13 Mo3 and Ti11 Mo5 show that the stability of Ti-Mo alloy increases with the increase of Mo element, and the modulus of elasticity of B, E and G all increase.